Speaker: Todd Kemp
Affiliation: Cornell University,
Title:
Haagerup inequalities in free probability
Time and Place: Monday, 2/6, 3:00-3:55pm, Milner 216.
Abstract:
In 1978, Uffe Haagerup introduced what has become known as the Haagerup
inequality: a functional inequality relating convolution norm and l^2
norm in the Free group factor. The Haagerup inequality has been used in
Lie theory (rapid decay), random walks (return probabilities), and
non-commutative geometry (Baum-Connes conjecture), just to name a few
applications.
In this talk, I will discuss the Haagerup inequality in free probability.
The original inequality fits into the natural framework of an important
class of free random variables called R-diagonal elements (which includes
both circular elements and Haar unitaries). I will address some of my
recent joint work with Roland Speicher, in which we prove a strengthened
version of the Haagerup inequality in the context of R-diagonal elements.
The techniques we use involve interesting combinatorics, and so this work
may be of interest both to functional analysts and combinatorialists.